# Question

Lucky Smokes currently operates a warehouse that serves the Virginia market. Some trucks arrive at the warehouse filled with goods to be stored in the ware- house. Other trucks arrive at the warehouse empty to be loaded with goods. Based on the number of trucks that arrive at the warehouse in a week, the firm is able to accurately estimate the total number of labor hours that are required to finish all of the loading and unloading. The following histogram plots these estimates for each week over the past two

years. (There are a total of 104 weeks recorded in the graph.) For example, there were three weeks in this period that required 600 total labor hours and only one week that recorded 1,080 hours of required labor. The mean of the data is 793 and the standard deviation is 111. Labor is the primary variable cost in the operation of a warehouse. The Virginia warehouse employed 20 workers, who were guaranteed at least 40 hours of pay per week. Thus, in weeks with less than 800 hours of required labor, the workers either went home early on some days or were idle. On weeks with more than 800 hours of required labor, the extra hours were obtained with overtime. Workers were paid time and a half for each hour of overtime. You have been placed in charge of a new warehouse scheduled to serve the North Carolina market. Marketing suggests that the volume for this warehouse should be comparable to the Virginia warehouse. Assume that you must pay each worker for at least 40 hours of work per week and time and a half for each hour of overtime. Assume there is no limit on overtime for a given week. Further, assume you approximate your workload requirement with a normal distribution.

a. If you hire 22 workers, how many weeks a year should you expect to use overtime?

b. If you hire 18 workers, how many weeks a year will your workers be underutilized?

c. If you are interested in minimizing your labor cost, how many workers should you hire (again, assuming your workload forecast is normally distributed)?

d. You are now concerned the normal distribution might not be appropriate. For example, you can't hire 20.5 workers. What is the optimal number of workers to hire if you use the empirical distribution function constructed with the data in the above histogram?

years. (There are a total of 104 weeks recorded in the graph.) For example, there were three weeks in this period that required 600 total labor hours and only one week that recorded 1,080 hours of required labor. The mean of the data is 793 and the standard deviation is 111. Labor is the primary variable cost in the operation of a warehouse. The Virginia warehouse employed 20 workers, who were guaranteed at least 40 hours of pay per week. Thus, in weeks with less than 800 hours of required labor, the workers either went home early on some days or were idle. On weeks with more than 800 hours of required labor, the extra hours were obtained with overtime. Workers were paid time and a half for each hour of overtime. You have been placed in charge of a new warehouse scheduled to serve the North Carolina market. Marketing suggests that the volume for this warehouse should be comparable to the Virginia warehouse. Assume that you must pay each worker for at least 40 hours of work per week and time and a half for each hour of overtime. Assume there is no limit on overtime for a given week. Further, assume you approximate your workload requirement with a normal distribution.

a. If you hire 22 workers, how many weeks a year should you expect to use overtime?

b. If you hire 18 workers, how many weeks a year will your workers be underutilized?

c. If you are interested in minimizing your labor cost, how many workers should you hire (again, assuming your workload forecast is normally distributed)?

d. You are now concerned the normal distribution might not be appropriate. For example, you can't hire 20.5 workers. What is the optimal number of workers to hire if you use the empirical distribution function constructed with the data in the above histogram?

## Answer to relevant Questions

You are traveling abroad and have only American dollars with you. You are currently in the capital but you will soon be heading out to a small town for an extended stay. In the town, no one takes credit cards and they only ...Shelf space in the grocery business is a valuable asset. Every good supermarket spends a significant amount of effort attempting to determine the optimal shelf space allocation across products. Many factors are relevant to ...A Cold Inc. is a frozen food distributor with 10 warehouses across the country. Iven Tory, one of the warehouse managers, wants to make sure that the inventory policies used by the warehouse are minimizing inventory while ...A small economic consulting firm has four employees, Alice, Bob, Cathy, and Doug. The firm offers services in four distinct areas, Quotas, Regulation, Strategy, and Taxes. At the current time Alice is qualified for Quotas, ...Consider the example of the Park Hyatt Philadelphia discussed in the text. Recall that the full fare is $225, the expected full-fare demand is Poisson with mean 27.3, the discount fare is $159, and there are 118 king/queen ...Post your question

0